Simulation of Nonequilibrium Dynamics on a Quantum Computer

Lamm, Henry; Lawrence, Scott

doi:10.1103/physrevlett.121.170501

Cited by 141 publications

(110 citation statements)

References 20 publications

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“…SU (2) has only three crystal-like subgroups: the binary tetrahedral, BT, the binary octahedral, BO, and the binary icosohedral, BI. Using the Metropolis algorithm with 100 measurements separated by 1000 updates, we refined the results of [23], finding that while BT has β f = 2.24 (8), BO and BI have β f = 3.26 (8) and β f = 5.82(8) respectively, both deep in the scaling regime β 2.2. Hence, these two last groups can be used in lieu of SU (2) for practical calculations.…”

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confidence: 99%

Gluon field digitization for quantum computers

et al. 2019

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Simulations of gauge theories on quantum computers require the digitization of continuous field variables. Digitization schemes that uses the minimum amount of qubits are desirable. We present a practical scheme for digitizing SU (3) gauge theories via its discrete subgroup S(1080). The S(1080) standard Wilson action cannot be used since a phase transition occurs as the coupling is decreased, well before the scaling regime. We proposed a modified action that allows simulations in the scaling window and carry out classical Monte Carlo calculations down to lattice spacings of order a ≈ 0.08 fm. We compute a set of observables with sub-percent precision at multiple lattice spacings and show that the continuum extrapolated value agrees with the full SU (3) results. This suggests that this digitization scheme provides sufficient precision for NISQ-era QCD simulations.

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confidence: 99%

Gluon field digitization for quantum computers

et al. 2019

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“…Another potentially interesting direction to look at is the digital quantum simulation of bosonic systems, for which limited literature still exists, and where it might turn out to be useful considering the quantum circuit model for the algorithmic solution of a single harmonic oscillator . Simulating the digitized non‐unitary evolution of an open quantum system on a quantum computer is a further topic of current interest . Finally, the huge body of knowledge accumulated in the past half a century to classically simulate the many body dynamics of quantum systems of increasing complexity, such as quantum Monte‐Carlo, molecular dynamics, and density matrix renormalization group could be integrated into quantum algorithms to be run on digital quantum computers, with far‐reaching and still unknown consequences.…”

Section: Outlook and Perspectivesmentioning

confidence: 99%

Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives

et al. 2019

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The past few years have witnessed the concrete and fast spreading of quantum technologies for practical computation and simulation. In particular, quantum computing platforms based on either trapped ions or superconducting qubits have become available for simulations and benchmarking, with up to few tens of qubits that can be reliably initialized, controlled, and measured. The present Review aims at giving a comprehensive outlook on the state‐of‐the‐art capabilities offered from these near‐term noisy devices as universal quantum simulators, that is, programmable quantum computers potentially able to calculate the time evolution of many physical models. First, a pedagogic overview on the basic theoretical background pertaining digital quantum simulations is given, with a focus on hardware‐dependent mapping of spin‐type Hamiltonians into the corresponding quantum circuit as a key initial step toward simulating more complex models. Then, the main experimental achievements obtained in the last decade are reviewed, focusing on the digital quantum simulation of such spin models by employing two leading quantum architectures. Their performances are compared, and future challenges are outlined, also in view of prospective hybrid technologies, towards the ultimate goal of reaching the long‐sought quantum advantage for the simulation of complex many‐body models in the physical sciences.

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“…Numerical lattice gauge theory started in the late 70's by studying Z 2 (Ising) gauge theories on 3 4 lattices and has steadily developed as a reliable tool that today allows different collaborations to compare numerical estimates for hadronic processes with errors of a few percent. It thus seems natural to start the study of real time evolution using the quantum Ising model in 1+1 dimension [5] or the Schwinger model [2,4].…”

Section: Introductionmentioning

confidence: 99%

Quantum simulation of scattering in the quantum Ising model

2019

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We discuss real time evolution for the quantum Ising model in one spatial dimension with Ns sites. In the limit where the nearest neighbor interactions J in the spatial directions are small, there is a simple physical picture where qubit states can be interpreted as approximate particle occupations. Using exact diagonalization, for initial states with one or two particles, we show that for small J, discrete Bessel functions provide very accurate expressions for the evolution of the occupancies corresponding to initial states with one and two particles. Boundary conditions play an important role when the evolution time is long enough. We discuss a Trotter procedure to implement the evolution on existing quantum computers and discuss the error associated with the Trotter step size. We discuss the effects of gate and measurement errors on the evolution of one-and two-particle states using 4 and 8 qubits circuits approximately corresponding to existing or near term quantum computers.

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Simulation of Nonequilibrium Dynamics on a Quantum Computer

Cited by 141 publications

References 20 publications

Gluon field digitization for quantum computers

Gluon field digitization for quantum computers

Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives

Quantum simulation of scattering in the quantum Ising model

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